scipy.linalg.

toeplitz#

scipy.linalg.toeplitz(c, r=None)[source]#

Construct a Toeplitz matrix.

The Toeplitz matrix has constant diagonals, with c as its first column and r as its first row. If r is not given, r == conjugate(c) is assumed.

The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details.

Parameters:

carray_like: First column of the matrix.
rarray_like, optional: First row of the matrix. If None, r = conjugate(c) is assumed; in this case, if c[0] is real, the result is a Hermitian matrix. r[0] is ignored; the first row of the returned matrix is [c[0], r[1:]].

Returns:

A(len(c), len(r)) ndarray: The Toeplitz matrix. Dtype is the same as (c[0] + r[0]).dtype.

See also

circulant: circulant matrix
hankel: Hankel matrix
solve_toeplitz: Solve a Toeplitz system.

Notes

The behavior when c or r is a scalar, or when c is complex and r is None, was changed in version 0.8.0. The behavior in previous versions was undocumented and is no longer supported.

Examples

>>> from scipy.linalg import toeplitz
>>> toeplitz([1,2,3], [1,4,5,6])
array([[1, 4, 5, 6],
       [2, 1, 4, 5],
       [3, 2, 1, 4]])
>>> toeplitz([1.0, 2+3j, 4-1j])
array([[ 1.+0.j,  2.-3.j,  4.+1.j],
       [ 2.+3.j,  1.+0.j,  2.-3.j],
       [ 4.-1.j,  2.+3.j,  1.+0.j]])